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David wrote in response to Hugh:
I'm not denying that you _can_ say that you had breakfast and lunch in
the same place. I'm arguing that it's not valid, geometrically to do so.
When you (the moving observer) determine the spatial distance between
breakfast and lunch at lunchtime, you put the breakfast end of the tape
measure at San Diego, not Los Angeles, and the lunch end of the tape
measure at San Diego. The Los Angeles observers put the breakfast end of
the tape measure at Los Angeles and the lunch end of the tape measure at
San Diego. The locations, in space, of breakfast at the time of lunch,
are what both frames consider to have been the locations of breakfast,
at the time of breakfast, since both frames say that the locations have
not changed, in their frame, since the time of breakfast.
Which strikes me (except for the last sentence below) as a quasi-proof of
John M's statement
<JM> "Clearly then, the spatial distance between two events is a
frame-dependent quantity."
These locations don't coincide in space, thus, they don't coincide in
spacetime.
Above you just "proved" that the two events coincide in space for F' but not
for F. So this last statement contradicts your above reasoning.
Joel R.